Document Type
Conference Proceeding
Publication Date
10-1-2012
Publication Title
Computational Geometry: Theory and Applications
Abstract
Motivated by constraint-based CAD software, we develop the foundation for the rigidity theory of a very general model: the body-and-cad structure, composed of rigid bodies in 3D constrained by pairwise coincidence, angular and distance constraints. We identify 21 relevant geometric constraints and develop the corresponding infinitesimal rigidity theory for these structures. The classical body-and-bar rigidity model can be viewed as a body-and-cad structure that uses only one constraint from this new class. As a consequence, we identify a new, necessary, but not sufficient, counting condition for minimal rigidity of body-and-cad structures: nested sparsity. This is a slight generalization of the well-known sparsity condition of Maxwell. © 2012 Elsevier B.V. All rights reserved.
Keywords
Computer aided design, Geometric constraint system, Rigidity theory
Volume
45
Issue
8
First Page
385
Last Page
405
DOI
10.1016/j.comgeo.2010.06.003
ISSN
09257721
Rights
© 2009 ACM
Recommended Citation
Haller, Kirk; Lee-St.john, Audrey; Sitharam, Meera; Streinu, Ileana; and White, Neil, "Body-and-Cad Geometric Constraint Systems" (2012). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/233
Comments
Archived as published.